if i have a matrix A how do i put it in upper triangular form??
arh let me refine my question if i have matrix A,
PA(P^-1)=B , where B is upper triangular matrix, but what is P?
i realised P contains eigenvectors as columns. but i stumble up as P has no inverse and it drives me mad and now im going to bed.
Are you talking about finding the Jordan Canonical Form of the matrix? If your working over a field that contains all of the eigenvalues of the matrix (the complex numbers are algebraicly closed, so this is a good one to work in) you can represent the matrix into one that is zero everywhere except possibly the diagonal and 1st superdiagonal.
The matrix P consists of the basis for the eigenspace of each of the Jordan blocks. In particular if you have all distinct eigenvalues, each eigenspace is one dimensional and your P matrix is just the corresponding eigenvectors and it will transform it into a diagonal matrix with the eigenvalues on the diagonal.
Not really sure if this is what you are talking about, but hope it helps.